A304654 a(n) = (n!)^2 * Sum_{k=1..n-1} 1/(k^2*(n-k)).

0, 0, 4, 27, 328, 6500, 192216, 7952112, 438941952, 31185057024, 2772643115520, 301622403456000, 39413353102848000, 6091955683706880000, 1099401414283210752000, 229088914497045356544000, 54589580461769879715840000, 14750581694440372638842880000

Offset

0,3

Links

Table of n, a(n) for n=0..17.

Formula

Recurrence: (2*n - 3)*a(n) = (6*n^3 - 25*n^2 + 33*n - 12)*a(n-1) - (n-2)^2*(6*n^3 - 29*n^2 + 42*n - 15)*a(n-2) + (n-3)^3*(n-2)^3*(2*n - 1)*a(n-3).

a(n)/(n!)^2 ~ Pi^2/(6*n).

Mathematica

Table[(n!)^2 * Sum[1/(k^2*(n-k)), {k, 1, n-1}], {n, 0, 20}]

Crossrefs

Cf. A052517, A302827, A304589, A304655.

Sequence in context: A119820 A159599 A221411 * A203202 A320961 A239726

Adjacent sequences: A304651 A304652 A304653 * A304655 A304656 A304657

Keyword

nonn

Author

Vaclav Kotesovec, May 16 2018

Status

approved